Energy evaluation using fast Fourier transforms (FFTs) enables sampling billions of putative complex structures and hence revolutionized rigid protein–protein docking. However, in current methods, efficient acceleration is achieved only in either the translational or the rotational subspace. Developing an efficient and accurate docking method that expands FFT-based sampling to five rotational coordinates is an extensively studied but still unsolved problem. The algorithm presented here retains the accuracy of earlier methods but yields at least 10-fold speedup. The improvement is due to two innovations. First, the search space is treated as the product manifold >S>O(>3) × (>S>O(>3)∖>S>1), where >S>O(>3) is the rotation group representing the space of the rotating ligand, and (>S>O(>3)∖>S>1) is the space spanned by the two Euler angles that define the orientation of the vector from the center of the fixed receptor toward the center of the ligand. This representation enables the use of efficient FFT methods developed for >S>O(>3). Second, we select the centers of highly populated clusters of docked structures, rather than the lowest energy conformations, as predictions of the complex, and hence there is no need for very high accuracy in energy evaluation. Therefore, it is sufficient to use a limited number of spherical basis functions in the Fourier space, which increases the efficiency of sampling while retaining the accuracy of docking results. A major advantage of the method is that, in contrast to classical approaches, increasing the number of correlation function terms is computationally inexpensive, which enables using complex energy functions for scoring.
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机译：使用快速傅里叶变换（FFT）进行能量评估，可以对数十亿个假定的复杂结构进行采样，从而彻底改变了刚性蛋白质与蛋白质的对接。但是，在当前方法中，仅在平移或旋转子空间中才能实现有效的加速。开发一种有效且准确的对接方法，可以将基于FFT的采样扩展到五个旋转坐标，这是一项经过广泛研究但仍未解决的问题。这里介绍的算法保留了较早方法的准确性，但产生了至少10倍的加速。改进归因于两项创新。首先，将搜索空间视为产品流形> S > O （> 3 ）×（> S > O （> 3 ）∖> S > 1 ），其中> S > O （> 3 ）是代表旋转配体空间的旋转组，而（> S > O （< strong> 3 ）∖> S > 1 ）是两个欧拉角所跨越的空间，两个角度定义了从固定受体的中心朝向配体的中心。这种表示形式可以使用针对> S > O （> 3 ）开发的高效FFT方法。其次，我们选择对接结构的人口稠密簇的中心而不是最低的能量构象作为复合物的预测，因此，在能量评估中不需要非常高的准确性。因此，在傅立叶空间中使用有限数量的球基函数就足够了，这在保持对接结果精度的同时提高了采样效率。该方法的主要优点是，与经典方法相比，增加相关函数项的数量在计算上不昂贵，这使得可以使用复杂的能量函数进行评分。
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